SPINODAL NUCLEATION

Abstract

The aim of this paper is to present the theoretical foundations of spinodal nucleation, by reviewing key theoretical and numerical work. The basic ideas of classical nucleation theory are first presented: the classical droplet model, and the Becker-Döring theory, as these concepts are important to the development of the field theoretical formulation of nucleation. The field theoretical framework for classical nucleation is exposed in some detail, followed by the presentation of a similar framework, extended to nucleation in the proximity of a spinodal (non-classical nucleation), in the presence of long-range Ising interactions. The non-classical nucleating droplet is found to be diffuse, hence to strongly depart from the classical prediction of a compact object with a well-defined surface. The fact that the non-classical nucleating droplet is identified with a ramified object prompts the development of an appropriate cluster description. The basic principles of percolation theory are outlined, and some lattice percolation models introduced. The Kastaleyn-Fortuin mapping, which establishes a connection between a particular percolation model and a limit of the Potts model, is briefly described. This mapping is crucial to the development of a second mapping (Coniglio-Klein) of the Ising spinodal point into a percolation model, where the long-range Ising interactions are translated into a long-range connectivity in the appropriate percolation model. The final result consists of the most powerful tool available to identify precisely the non-classical nucleating droplet in numerical simulations of nucleation in proximity of a spinodal. Numerical simulation results are presented, which support the field theoretical formulation of non-classical nucleation. As the numerical results seem to support the fact that the non-classical nucleating droplet is also a percolation cluster, its fractal structure is investigated by considering the mean-field regime of the percolation model, i.e. a percolation model with long-range connectivity. This leads to an apparent contradiction between the field theory and the mean-field percolation model predictions concerning the mass (or density) scaling of the nucleating droplet. This inconsistency is resolved by postulating that the mean-field percolation clusters cannot be non-classical nucleating droplets, and proposing that the non-classical nucleating droplet is in fact the result of a coalescence of many such clusters. Finally, the calculation of the static prefactor in the nucleation rate by assuming a Becker-Döring dynamics for the coalescence mechanism is outlined. The result is found to be consistent with the predictions of the field theory for the static prefactor. Numerical results are also presented in support of the hypothesized coalescence mechanism.